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For any sets A and B, their cardinal numbers satisfy |A|<=|B| iff there is a one-to-one function f from A into B (Rubin 1967, p. 266; Suppes 1972, pp. 94 and 116). It is easy ...

The term "closure" has various meanings in mathematics. The topological closure of a subset A of a topological space X is the smallest closed subset of X containing A. If R ...

Given two topological spaces M and N, place an equivalence relationship on the continuous maps f:M->N using homotopies, and write f_1∼f_2 if f_1 is homotopic to f_2. Roughly ...

A set S and a binary operator * are said to exhibit closure if applying the binary operator to two elements S returns a value which is itself a member of S. The closure of a ...

There are (at least) two graphs associated with Ellingham and Horton. These graphs on 54 and 78 nodes respectively, illustrated above, are examples of 3-connected bicubic ...

The Johnson solids are the convex polyhedra having regular faces and equal edge lengths (with the exception of the completely regular Platonic solids, the "semiregular" ...

Riddell's formula for unlabeled graphs is the Euler transform relating the number of unlabeled connected graphs on n nodes satisfying some property with the corresponding ...

A cubic map is three-colorable iff each interior region is bounded by an even number of regions. A non-cubic map bounded by an even number of regions is not necessarily ...

A matrix for a round-robin tournament involving n players competing in n(n-1)/2 matches (no ties allowed) having entries a_(ij)={1 if player i defeats player j; -1 if player ...

A tripod is a tree having exactly three tree leaves (Pirnazar and Ullman 2002). The numbers of tripods on n=1, 2, ... vertices are 0, 0, 0, 1, 1, 2, 3, 4, 5, 7, 8, 10, 12, ...